Re: ECC point compression trick


Tom St Denis wrote:
Think about what mm said ... why can't we just always use one of the
roots?

e.g. you have

y == +/- sqrt(x^3 - 3x + b)

Why not always just use the positive root [adjusting your secret
multiplier as required since (-k)P == k(-P)].

May I suggest that read a text on Finite Fields?
The one by Lidl & Neiderreiter is superb.

You are working in a (multiplicative sub-group of a) finite field.

There is no canonical way to order elements so as to
distinguish "positive" from "negative".

The square roots of 2 mod 7 are 3 and 4.

Please tell me which one is the postive root and which one is the
negative? If you always want to (say) always select the one with
larger norm and declare it as 'positive', tell us how to do this over
an extension field and not just in the ground field.

.

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